Class Notes May 8

Summary of Tuesday May 8, 2001 ATM S 560 lecture 						Sarah Gaichas

Dynamics of ENSO (cont): The ENSO mode and  Delayed Oscillator Theory  (DOT)

We began the lecture by reviewing the progression from simple, unbounded,
homogenous basic state coupled ocean atmosphere models to the more realistic
intermediate coupled models.  Intermediate models are characterized by an
inhomogeneous basic state (e.g., cold tongue, zonal SST gradient and
difference in thermocline depth) and the inclusion of an ocean surface mixed
layer (~50m) to permit more rapid reactions of SST to changes in thermocline
depth.  These intermediate models produce ENSO-like variability in terms of
near-equatorial SST and winds, with warm events peaking during Northern
Hemisphere winter and occurring with (overly) regular 3-4 year periodicity.
All this with basically linear physics .

ENSO is thus described as a true mode of the coupled ocean-atmosphere system
in the equatorial Pacific, representing a balance between a Bjerknes
feedback in the Eastern half of the tropical Pacific (wind alters SST
gradient alters wind, etc) and a delayed ocean adjustment (via Rossby and
reflected Kelvin signals of changing amplitude) in the Western Pacific.
This is the progression (starting with the initiation of a warm phase):

First, the easterly trades relax in the central Pacific. This disturbance
sends a Kelvin wave to the east (at the speed of a gravity wave), which
deepens the thermocline there, so that upwelled water is anomalously warm.
At the same time, Rossby waves propagate towards the west from the central
Pacific, at a maximum speed of 1/3 of Kelvin wave speed for the gravest
Rossby mode (the difference in speed seems key, as it allows the signals to
propagate for a while without interference?).  The Rossby signals raise the
thermocline in the western Pacific (but not enough to alter SST by much-most
of the SST anomaly signal is in the eastern Pacific). The Kelvin-deepened
thermocline in the east increases SST in the eastern Pacific via upwelling of
warmer water, decreasing the zonal SST gradient, and therefore further
weakening the surface easterly winds, so that the forcing for the Kelvin and
Rossby signals from the central Pacific continues, and propagates waves of
increasing amplitudes.  However, at the same time the initial signals are
reflected when they hit their respective boundaries.  We saw in previous
lectures that the Kelvin wave reaching the eastern boundary is perfectly
reflected below the critical latitude (dependent on frequency-lower
frequency, higher critical latitude) so that nearly 100% of its initial
energy returns as (inverse) Rossby modes back towards the west, which also
deepen the thermocline.  At the western boundary, at most 50% of the initial
energy from the gravest Rossby mode is reflected back to the east as an
(inverse) Kelvin mode, which tends to raise the thermocline.  Close to the
boundaries, these reflected signals are moving the thermocline in the same
direction as the signals originating in the central Pacific.  By the time
the reflected Kelvin signal reaches the central pacific, however, it tends
to move the thermocline up while the weakened easterly or even westerly
surface winds are still forcing Kelvin energy to the east that wants to
deepen the thermocline.  The first reflected Kelvin mode arriving from the
west is the weakest, so it loses its battle with the wind.  However, because
the system is continuously forced via the Bjerkness feedback in the east,
subsequent reflected Kelvin signals from the west will be stronger.  At the
same time, considerable heat has been lost from the ocean in the east where
the SST anomalies are large, thus strengthening the weakened zonal SST
gradient and tending to strengthen surface winds. The system reaches a point
where the reflected Kelvin energy from the west is strong enough to raise the
thermocline from the central to eastern Pacific when the heat loss from the
ocean in the east has also weakened the anomalous surface winds.  In the
ensuing turnover to cold phase, the raised thermocline in the east brings
cooler water into the surface layer via upwelling, cooling SST and
re-establishing the zonal SST gradient, fueling stronger easterly trade
winds, which set up the reverse dynamics.  With opposite wind stress, Kelvin
and Rossby signals still propagate to the east and west, respectively, but
with opposite signs (ie Kelvin waves raise the thermocline and Rossby modes
lower it).

So to end the cold phase and initiate the warm phase, we conclude that
reflected Kelvin waves from the western border will want to lower the
thermocline, and do battle with the easterlies until they win, and the winds
weaken.

[Is it ever the reflected Rossby signal from the eastern boundary that
contributes to this? How do these signals interact? Ans: YES, the eastern
reflection is important.  We didn't focus on it when discussing the
so-called delayed oscillator physics because it is subsumed into the
Bjerknes Mechanism. However, the eastern boundary reflected Rossby signals
are important, as they effect SST in the eastern half of the basin.]


Now that we have the basic ingredients down, what sets up the (irregular) 3+
year periodicity of the cycle, and the linkage with seasonality (events
tendency to peak at the end of the calendar year)?  

One major question is whether the observed interaction of ENSO with the
seasonal cycle can (should) be explained by nonlinear or linear dynamics.  

So now on to the subject of the lecture the Delayed Oscillator equation, and
the ENSO mode as described by linear analysis. The key concept is the two
different timescales for the Bjerkness feedback vs. the ocean adjustment,
and how they are related. The delayed oscillator equation relates the rate
of change in eastern Pacific temperature anomaly to the local atmosphere
ocean feedback minus the lagged ocean adjustment, which depends on
dissipation of Rossby signals and how much energy is reflected at the
boundaries.  The equation can be parameterized to produce ENSO-like behavior
via nonlinear dynamics by emphasizing local feedback over ocean adjustment
(and allowing a nonlinear temperature anomaly term), or it can produce ENSO
behavior with linear dynamics by allowing the delayed ocean adjustment term
to exceed the local feedback term.  

In this lecture, we also examined a purely linear coupled ocean atmosphere
model where the ENSO mode falls neatly out of an eigenvalue analysis (aka
Floquet analysis).  Here, the (linearized) equations representing the
dynamics of the system were evaluated with monthly climatological mean
fields to produce propagator matrices, which could be composed (multiplied)
to determine the change in states between any number of months.  An analysis
was conducted by multiplying all the monthly matrices for a year to arrive
at an annual matrix such that the eigenvalues (called Floquet multipliers)
of this (eg, January to December) propagator matrix indicate frequencies
growth rates for the eigenvectors of the annual matrix.  The eigenvectors
are the modes of the coupled system, and the only eigenvector (associated
with the dominant eigenvalue or Floquet multiplier) that grows in this
system is the ENSO mode.  (Different configurations of the year propagator
matrix beginning and ending with different months will produce slightly
different eigenvectors which all look like ENSO in one form or another; the
eigenvalues and therefore growth rates of the modes remain the same
regardless of start and end month.)  An interesting feature of the model is
that the ENSO mode appears whether an annual climatological mean is used or
monthly varying climatologies are introduced using the multiplied monthly
propagators.  The inclusion of the annual cycle produces more variability in
the timing of the cycle as well as ENSO peaks in the N. hemisphere winter,
which is more consistent with observations than the annual mean model.  

We then briefly compared the linear modeling results with some of the
observations of ENSO.  In terms of heat content evolution, and the onset,
growth, and decay of a warm event, these results are basically consistent
with both observations and hindcasts from ocean GCMs.  There is also
consistency with interannual variability predicted in coupled GCMs.  It
appears clear in observations that warm events contain the seeds of their
own destruction in the form of the Rossby and reflected Kelvin signals.
These show up as slowly propagating west to east signals that lead to a
sudden change in thermocline depth in the eastern half of the basin.  What
is not clear from observations is how warm events arise from the ashes of
the previous cold event.

We concluded by discussing the implications of this.  We have seen that you
can get the basic characteristics of the system with purely linear physics,
but we also know there are nonlinearities in the system because there is
considerable skewness in the observations (warm events are stronger than
cold events).  The question then, is whether the system is primarily linear
with some secondary nonlinear embroidery that shows up to confuse matters
slightly in the observations, or whether this is an inherently nonlinear
system that we can coincidentally imitate pretty well with linear
approximations.  Where the distinction matters is in our ability to predict
ENSO events.